STATS 506 Problem Set #5

Author

Haiming Li

OOP Programming

  1. Here’s the inclusion of gcd and lcm method using Rcpp
library(Rcpp)
Warning: package 'Rcpp' was built under R version 4.3.3
cppFunction('
#include <numeric>
int gcd(int a, int b) {
  return std::gcd(a, b);
}')

cppFunction('
#include <numeric>
int lcm(int a, int b) {
  return std::lcm(a, b);
}
')

Here’s the class definition and class methods.

setClass('rational',
         slots = list(numerator = 'integer', 
                      denominator = 'integer'))

##' Constructor
##' @param numerator An integer value
##' @param denominator An none zero integer value
##' @return
##' @export
rational <- function(numerator = 0, denominator = 1) {
  if (!is.numeric(numerator) | !is.numeric(denominator)) {
    stop('both numerator and denominator must be integer')
  }
  if (numerator != as.integer(numerator) | 
      denominator !=as.integer(denominator)) {
    stop('both numerator and denominator cannot be floating point')
  }
  return(new('rational', numerator = as.integer(numerator), 
      denominator = as.integer(denominator)))
}

setValidity('rational', function(object){
  if (object@denominator == 0L) {
    stop('denominator cannot be 0')
  }
  return(TRUE)
})
Class "rational" [in ".GlobalEnv"]

Slots:
                              
Name:    numerator denominator
Class:     integer     integer
setMethod('show', 'rational',
          function(object) {
            cat(object@numerator, '/', object@denominator, '\n')
            return(invisible(object))
          })

setGeneric('simplify', function(object) standardGeneric('simplify'))
[1] "simplify"
setMethod('simplify', 'rational', function(object) {
  # compute the unsigned greatest common divisor
  divisor <- gcd(abs(object@numerator), abs(object@denominator))
  # simplify the fraction and sign
  new_num <- object@numerator / divisor
  new_den <- object@denominator / divisor
  if (new_num < 0 & new_den < 0) {
    new_num <- abs(new_num)
    new_den <- abs(new_den)
  }
  return(rational(new_num, new_den))
})

setGeneric('quotient', function(object, digits = 4) standardGeneric('quotient'))
[1] "quotient"
setMethod('quotient', 'rational', function(object, digits = 1) {
  # round() will floor the digits if it's not integer
  if (!is.numeric(digits) | digits < 0) {
    stop('digit must be none negative real number')
  }
  quotient_value <- object@numerator / object@denominator
  print(round(quotient_value, digits))
  return(invisible(quotient_value))
})

setMethod('+', signature(e1 = 'rational', e2 = 'rational'), function(e1, e2) {
  denom <- lcm(e1@denominator, e2@denominator)
  numer <- (e1@numerator * (denom / e1@denominator)) + 
    (e2@numerator * (denom / e2@denominator))
  return(simplify(rational(numer, denom)))
})

setMethod('-', signature(e1 = 'rational', e2 = 'rational'), function(e1, e2) {
  denom <- lcm(e1@denominator, e2@denominator)
  numer <- (e1@numerator * (denom / e1@denominator)) - 
    (e2@numerator * (denom / e2@denominator))
  return(simplify(rational(numer, denom)))
})

setMethod('*', signature(e1 = 'rational', e2 = 'rational'), function(e1, e2) {
  numer <- e1@numerator * e2@numerator
  denom <- e1@denominator * e2@denominator
  return(simplify(rational(numer, denom)))
})

setMethod('/', signature(e1 = 'rational', e2 = 'rational'), function(e1, e2) {
  numer <- e1@numerator * e2@denominator
  denom <- e1@denominator * e2@numerator
  if (denom == 0L) stop('division by zero')
  return(simplify(rational(numer, denom)))
})
  1. Here’s the demonstration
r1 <- rational(24, 6)
r2 <- rational(7, 230)
r3 <- rational(0, 4)
r1
24 / 6 
r3
0 / 4 
r1 + r2
927 / 230 
r1 - r2
913 / 230 
r1 * r2
14 / 115 
r1 / r2
920 / 7 
r1 + r3
4 / 1 
r1 * r3
0 / 1 
r2 / r3
Error in r2/r3: division by zero
quotient(r1)
[1] 4
quotient(r2)
[1] 0
quotient(r2, digits = 3)
[1] 0.03
quotient(r2, digits = 3.14)
[1] 0.03
quotient(r2, digits = 'avocado')
Error in quotient(r2, digits = "avocado"): digit must be none negative real number
q2 <- quotient(r2, digits = 3)
[1] 0.03
q2
[1] 0.03043478
quotient(r3)
[1] 0
simplify(r1)
4 / 1 
simplify(r2)
7 / 230 
simplify(r3)
0 / 1
  1. Here’s the checking of malformed input to constructor
rational(1, 0)
Error in validityMethod(object): denominator cannot be 0
rational(3.14, 1)
Error in rational(3.14, 1): both numerator and denominator cannot be floating point
rational(1, 3.14)
Error in rational(1, 3.14): both numerator and denominator cannot be floating point
rational('A', 1)
Error in rational("A", 1): both numerator and denominator must be integer
rational(1, 'A')
Error in rational(1, "A"): both numerator and denominator must be integer

Plotly

  1. Here’s the recreation using plotly
library(tibble)
library(dplyr)
library(reshape2)
library(plotly)

# read & proces data (same as Pset4)
df <- as_tibble(read.csv('./df_for_ml_improved_new_market.csv'))
genre_columns <- grep('Genre___', colnames(df), value = TRUE)
genre_data <- df[, c('id', 'year', 'price_usd', genre_columns)] %>%
  melt(id.vars = c('id', 'year', 'price_usd')) %>%
  filter(value == 1) %>%
  mutate(genre=sub('Genre___', '', variable)) %>%
  select(id, year, price_usd, genre)

# Ex: If the genre is both 'Other' and 'Painting', the final genre should be
#     'Painting'
genre_priority <- c('Photography', 'Print', 'Sculpture', 'Painting', 'Others')
genre_data$genre <- factor(genre_data$genre, levels = genre_priority)
df <- genre_data[!duplicated(genre_data$id), 2:4]
genre_data <- df %>%
  count(year, genre) %>%
  group_by(year) %>%
  mutate(percent = n / sum(n))

plot_ly(data = genre_data, x = ~percent, y = ~year, color = ~genre,
        type = 'bar', orientation = 'h') %>%
  layout(
    barmode = 'stack',
    title = 'Genre Distribution Over Years',
    xaxis = list(title = 'Percentage'),
    yaxis = list(
      title = 'Year',
      tickmode = 'array',
      tickvals = unique(genre_data$year),
      ticktext = unique(genre_data$year),
      categoryorder = 'trace'
    ),
    legend = list(title = list(text = 'Genre'))
  )
  1. Here’s the interactive plot
plot_data <- df %>%
  group_by(year, genre) %>%
  summarize(avg_price_usd = mean(price_usd, na.rm = TRUE)) %>%
  ungroup()

traces <- list()

# overall trend
overall_trace <- plot_data %>%
  group_by(year) %>%
  summarize(avg_price_usd = mean(avg_price_usd, na.rm = TRUE))

traces[['Overall']] <- list(
  x = overall_trace$year,
  y = overall_trace$avg_price_usd,
  type = 'scatter',
  mode = 'lines+markers',
  name = 'Overall'
)

# genre-specific trend
genres <- unique(plot_data$genre)
for (genre in genres) {
  genre_trace <- plot_data %>% filter(genre == !!genre)
  
  traces[[genre]] <- list(
    x = genre_trace$year,
    y = genre_trace$avg_price_usd,
    type = 'scatter',
    mode = 'lines+markers',
    name = genre
  )
}

fig <- plot_ly()
for (trace_name in names(traces)) {
  fig <- fig %>%
    add_trace(
      x = traces[[trace_name]]$x,
      y = traces[[trace_name]]$y,
      type = traces[[trace_name]]$type,
      mode = traces[[trace_name]]$mode,
      name = trace_name,
      visible = ifelse(trace_name == 'Overall', TRUE, FALSE)
    )
}

# drop down menu
fig <- fig %>%
  layout(
    title = 'Change in Sales Price Over Time by Genre',
    xaxis = list(title = 'Year'),
    yaxis = list(title = 'Average Price (USD)'),
    updatemenus = list(
      list(
        buttons = lapply(names(traces), function(genre) {
          list(
            method = 'update',
            args = list(list(visible = sapply(names(traces), function(x) x == genre))),
            label = genre
          )
        }),
        direction = 'down',
        x = 0.08,
        y = 1.1
      )
    )
  )

fig